Sorry was a bit short before,
As the curve 1/(1 + x^2) is at 1 when x = 0 and at .5 when x = 1 you cant take the integral from 0 to 1 with respect to y. So take the integral from .5 to 1 and add the volume of the cylinder left, which r = 1, h = .5.
If you need anything more ill try write out...